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181005 ||| eng |
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|a 9780511978111
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| 050 |
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4 |
|a QA612.7
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|a Simpson, Carlos
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| 245 |
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|a Homotopy theory of higher categories
|c Carlos Simpson
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| 260 |
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|a Cambridge
|b Cambridge University Press
|c 2012
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| 300 |
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|a xviii, 634 pages
|b digital
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| 505 |
0 |
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|a Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction -- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization -- Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories -- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories -- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization
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| 653 |
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|a Homotopy theory
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| 653 |
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|a Categories (Mathematics)
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b CBO
|a Cambridge Books Online
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| 490 |
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|a New mathematical monographs
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| 856 |
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|u https://doi.org/10.1017/CBO9780511978111
|x Verlag
|3 Volltext
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| 082 |
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|a 512.62
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| 520 |
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|a The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others
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